A review is presented of the various contributions to the problem of accommodating cyclical production patterns when several products are made in a single facility. Recent contributions to its resolution resulted in either analytical approaches to a restricted problem, or heuristic approaches to the entire problem. This work also extends. The analysis is extended in the following four directions: (a) an improved analytical approach, (b) a test for feasibility, (c) a systematic means for escape from infeasibility, and (d) a procedure for the determination of a basic period for a given set of multipliers to achieve a feasible schedule.